I think the description of this rose as having "up to 40 petals" is almost certainly incorrect. Botanica's Roses describes it as "very double" and The American Rose Society's Encyclopedia of Roses as "brimming with petals". There are other, similar, descriptions in publications listed in the references section for this rose. My rose, which I believe I have now positively identified as 'Felicite et Perpetue' has 80+ petals. This being the case, there are several images in the photo section for this rose which are likely to have been incorrectly identified - their petals are much less numerous.
The references show various degrees of fullness: double 1880; well double 1914 1938; full 1838 1848 and 1873; very double 1847 1976, and fully double 1993. Bunyard's 1936 and Jedmar's 1890 illustrations are also quite full. I am inclined to agree with you that it should have more than 40 petals and have changed it to Very Full 41+ petals. However there is a slight niggle in that AmiRoses illustration does not appear to be all that full.
Henri-Antoine Jacques dedicated this rose to his daughters, Félicité and Perpétue (Felicity and Perpetua, so named in homage to the Christian martyrs who were martyred and put to death at Carthage during the 3rd century)
"It has been suggested since 1900 that Jacques named this rose after his own twin daughters, but so far I have found noo proof of twins, nor of children with these names. Anyway most French historians would find it out of keeping for the Head Gardener at that period to name a rose after his own family, considering that all the other ramblers were given Royal names." (Barbara Tchertoff, "Antoine Jaques – Head Gardener to Louis-Philippe" Part 1, page 30, in: ‘Historic Rose Journal’ No. 20, Autumn 2000)
Fallacies abound in the naming of roses. A British nursery markets Pemberton's 'Cornelia', 'Felicia' and 'Penelope' as 'The Vicar's daughters collection', claiming the varieties to be named after the breeder's three daughters. The Rev Pemberton lived his entire life in his ancestral family home, almost all of it with his spinster sister!